We have developed a method to calculate relative binding free energies for 5-10 ligands binding to the same protein from a single computer simulation. Our chemical-Monte Carlo/Molecular Dynamics calculations have been applied to study a family of nonnucleoside inhibitors of HIV reverse transcriptase (HIV-RT), and yielded free energies in good agreement with experiment. The Computer Graphics Laboratory graphics hardware and MidasPlus software are used to monitor our simulations.